Does the earth have a carrying capacity?  If so, what is the carrying capacity of the earth?

The definition that Cory quoted is good. However, he, and as far as I can tell almost all scientists that have contributed to wikipedia/overpopulation article, have failed to comprehend that definition. His numbers totally ignore a fundamental requirement of the definition sustainability. Burning oil, coal, natural gas, uranium, is permanent damage. Most see the burning of fossil fuels as permanent damage only because of the carbon dioxide that is produced, but that is a mistake. It is permanent damage simply because the oil, an asset, is being eliminated. You would not say that a corporation is sustainable if its savings account was being run down, right? I suspect that people, including scientists that should know better, are ignoring fossil fuel destruction because we don't eat fossil fuels. You'd think that if we only could eat leaves and we were eating them faster than the leaves grew, they would make it absolutely clear that we are overpopulated. What they and you should understand is that we don't have to directly eat the oil. We depend on it to create food for 7 billion. We might be able to provide for 8 billion as Cory suggests, but there is no reason to believe it could be sustained indefinitely. There is a huge difference between provide and sustain. Provide is a one time or short term concept. Sustain, is indefinitely. We are using countless resources faster than they renew. Oil, coal, uranium are just a few examples. We have no clue how to feed today's 7 billion without consuming those resources. We must use oil to plant, fertilize, harvest, package, store, and distribute 7 billion meals a day. This means that until we figure out how to feed ourselves with only renewable means, we don't know what the carrying capacity is. Furthermore, attempting to calculate how many people can be sustained is a waste of time and proves a lack of comprehension. To explain why, consider three possible situations. 1) go back in time to a period where we were not consuming resources that were essential to providing for our numbers faster than they renew. 2) use today's technology, economy, and human knowledge but eliminate the use of resources faster than they renew when calculating how many can be sustained, 3) use future technology, to determine the sustainable level. #3) is clearly idiotic because nobody has a clue what will be invented in the future. It would be incredibly arrogant to think you can calculate how many can be sustained by exchanging oil, coal, uranium energy sources with wind, solar, bio fuels. The world, including human economic and political interaction is much more complex than that simplistic calculation. No scientist should have the arrogance to think that they know what the environmental impact would be of huge solar and wind farms on the scale to eliminate the need for non-renewables. #2) is useless because we can't possibly get to that number with today's technology. Today's technology requires oil. The solution, limiting our births, will take time, and thus we cannot be at the population that is sustainable with today's knowledge. We will be there with some future knowledge. #1) Is the best because it was achieved, where-as #2, and #3 are theortical at best. Our numbers were below 1 billion the last time our numbers were provided for without consuming resources faster than they renew. We don't need to predict that carrying capacity. We must get our numbers down to the point where we are not consuming resources faster than they renew. See http://stopattwo.org for more information.

To answer this, one would need to specify whether we are talking about the carrying capacity with current levels of technology (versus allowing technology itself to evolve), and what degree of sustainability is needed. Assuming evolving technology, my best guess is that the carrying capacity is substantially greater than current world population. It could be 30 billion. It could be 1 trillion. To take the example  land occupied, consider this: http://www.persquaremile.com/2011/01/18/if-the-worlds-population-lived-in-one-city/ Conversely: http://econlog.econlib.org/archives/2008/12/dreaming_the_si.html As for food, a few cities with large hydroponic towers could generate enough food for the world. Regarding water and natural resources, obviously current usage patterns and technologies are not sustainable for a trillion-people world. But there are many alternative technologies that can be developed and will be if population is large enough. For some discussion, see this book: http://juliansimon.com/writings/Ultimate_Resource/

Undeniably, the Earth does have a carrying capacity. To answer your question simply, with the population's current growth rate we would hypothetically have over 10 billion people on Earth by 2050. However, the UN estimates we will peak around 8 billion people in 2041 and then decline. Therefore, the most widely accepted estimate for human carrying capacity of Earth is around 8 billion people (at current consumption rates). To put that in perspective, the latest official current world population estimate, for mid-year 2010, is estimated at 6,852,472,823 (http://about.com). Further explanation: Ecologists define 'carrying capacity' as “the population of a given species that can be supported indefinitely in a defined habitat without permanently damaging the ecosystem upon which it is dependent” (Rees). Human carrying capacity can then be understood as the maximum rate of resource consumption and waste discharged that can be sustained without damaging the environment beyond repair. We all want to live a happy and healthy life, yet to do this we need fresh water, food, and materials for shelter and security. However, the world is a finite place and there is a limit to the amount of available resources. How many people can the Earth support? Our carrying capacity varies depending on how much we consume. The question is: what standard of living is globally acceptable and how much are we willing to compromise? For instance, if everyone ate as much as Americans we would only be able to support 2.5 billion people. The Italians, on the other hand, live healthier lives with a much more varied diet, consuming half as much grain as Americans. They have longer life expectancies and at their level of consumption we could support roughly 5 billion people. (Brown) In order to meet that 8 billion people from the earlier estimate, we would have to eat somewhere between the average resident of India and the average Italian. This means a significant change in the American diet and a more efficient distribution of the available food on the planet. Basically: Eat enough, not too much, mostly fruits and vegetables. Only the future will tell what limit the Earth will have and what sacrifices people are willing to make for others survival. Sources: Brown, Lester (2008). Plan B 3.0: Mobilizing to Save Civilization. http://www.earth-policy.org/books/pb3 Rees, W. (1990). Sustainable development and the biosphere. http://geography.about.com/od/obtainpopulationdata/a/worldpopulation.htm

When most people talk about the carrying capacity of the world, the first issue that comes to mind is population and the use of limited resources that the world has to offer.  The answer and definition provided above by Cory demonstrates this exact mentality.  Although I agree with this information I and believe that we should be concerned about the consumption of vital resources, I think that the more significant issue is that of destruction.  The damage that we are doing to the planet is continuing to grow and global warming may just be the beginning.  Some companies around the world have already begun to search for ways to shrink their footprint but we should begin to think about the negative output that another 3 billion people would create.  According to http://garbage.wikidot.com, each year Americans create nearly 210 million tons of solid waste.  On average people throw away about 4 pounds of garbage a day per person.  So, when the world reaches the 10 billion people we will be producing approximately 40 billion pounds of garbage per day and 14.6 trillion pounds of trash per year.  Even if we find enough fuel to power all of our new technology and enough fresh water to hydrate 10 billion people what are we going to do with all the additional waste? We should be searching for cleaner sources of energy and we should be looking for ways to support greater amounts of people, but we also need to take another look at what happens after we consume these goods

It's debatable and the simple answer is we just don't know. The infographic below from Best Foot Forward illustrates this point by plotting all of the various estimates that have been suggested against our actual population. Sources are all at the bottom of the image.

When I was younger, I would go out to the barn and sometimes I would see a little field mouse run by. I have no idea how many mice there were in that barn. I suspect their population was pretty small though. One day I went to the barn and I saw 4 or 5 of the little rodents in the space of a few minutes. As I was poking around looking for the bag of seeds I had stowed away months before, I saw more and more of them. When I found the bag of seeds, I lifted it up and there must have been hundreds of mice that just came pouring out of that bag. Seriously...hundreds. They had gotten into my seed and were overpopulating like mad. So, what was the carrying capacity of my barn? The mice had taken advantage of a one time glut of non-renewable resources to prosper and reach a completely unsustainable population. Once those seeds were gone, they soon died out. It is a big mistake for us to think about a sustainable population size being anywhere near where it is now when the fundamental energy source making that population feasible is non-renewable, quickly being depleted and our use of it is changing the environment in which we currently exist into something that may be less habitable in the future.

Most of the answers are decidedly wrong, and the question carries an assumption that is unwarranted.  Carrying capacity isn't just about humans. The reason most answers are wrong is because they presume that humans are the only living things on this planet.  We already see how readily overfishing occurs.  We already see mass extinctions because of human presence and the destruction of ecosystems because of human resource demands.  Our current use of technology in GMOs is creating future problems we can't even envision.  Just as our use of antibiotics was careless resulting in the potential loss of one of our greatest assets in fighting disease, so to are we setting selection pressures on our greatest threats to food production.  If this follows a similar path, we may well find that we have created super-pests that are more responsive than our ability to twart them. We've already exceeded the Earth's carrying capacity.  The only question now is how many species go extinct, what vulnerabilities that does create for human civilization, and when do we finally fail because there's nothing else to exploit. Technology cannot save us.  At it's absolute best, it can only postpone the inevitable which, when it occurs, will be significantly more catastrophic than if we had addressed it initially.  At its core, the problem is that humans think that technology can allow them to be the exceptions.  That everything revolves around what humans want to do.  Like it or not, we are part the world at large, and we are doing our level best to destroy it and ourselves.

A little under 30 Billion by my reckoning.  I figured the land area at 57.5 million square miles, with about 40% capable of producing food.  That came to 23 Million Square miles, times 640 acres per Square mile = 14.72 Billion acres with 2 humans per acre, on average.  In my opinion this represents an optimistic best case scenario in terms of maximum population survivability.  In terms of acceptable quality of life, I would divide the number by 4.  You do the math on that.